Mathematics of NMR Shielding

This section works through the theory behind the NMR shielding calculation covered in How NMR Calculation Works, in more mathematical detail.

• The Nuclear Magnetic Shielding Tensor — how shielding is defined as a second derivative of the energy.
• The Gauge Origin Problem — why the choice of gauge origin matters, and where it goes wrong with finite basis sets.
• Gauge-Including Atomic Orbitals (GIAO) — how GIAO fixes the gauge origin problem.
• Coupled-Perturbed Equations for Shielding — solving for the field-dependent response of the wavefunction.
• Isotropic Shielding and Anisotropy — extracting physically meaningful numbers from the shielding tensor.
• Referencing Chemical Shifts — converting an absolute shielding constant into an experimentally comparable chemical shift.

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